What rate of interest is obtained from investing in (9)1/2 percent at par?

Options

A. `(9)1/2%`
B. `(8)1/2%`
C. `(18)2/3%`
D. none of these

Answer

To find the rate of interest obtained from investing in 9½ percent at par, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Terms**:
- "At par" means that the market value of the investment is equal to its face value. In this case, the face value is assumed to be 100.

2. **Identify the Given Values**:
- The nominal interest rate (or coupon rate) is 9½ percent, which can be expressed as a fraction:
\[ 9\frac{1}{2} = \frac{19}{2} \text{ percent} \]

3. **Set Up the Formula for Rate of Interest**:
- The formula to calculate the rate of interest when the investment is at par is:
\[ \text{Rate of Interest} = \left( \frac{\text{Nominal Rate}}{\text{Market Value}} \right) \times 100 \]

4. **Substitute the Values into the Formula**:
- Here, the nominal rate is \( 9\frac{1}{2} = 9.5 \) and the market value is 100:
\[ \text{Rate of Interest} = \left( \frac{9.5}{100} \right) \times 100 \]

5. **Calculate the Rate of Interest**:
- Simplifying the equation:
\[ \text{Rate of Interest} = 9.5 \text{ percent} \]

### Final Answer:
The rate of interest obtained from investing in 9½ percent at par is **9.5 percent**.

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